What is 1/(2sqrt(5)+2)-1/(2sqrt(5)-2) ?

The solution to 1/(2sqrt(5)+2)-1/(2sqrt(5)-2) is -1/4

Popular >

simplify 1/(2sqrt(5)+2)-1/(2sqrt(5)-2)

simplify

\frac{1}{2 5 + 2} - \frac{1}{2 5 - 2}

- \frac{1}{4}

Decimal Notation

- 0.25

Solution steps

\frac{1}{2 5 + 2} - \frac{1}{2 5 - 2}

Least Common Multiplier of

25 + 2, 25 - 2 : (25 + 2) (25 - 2)

Adjust Fractions based on the LCM

= \frac{2 5 - 2}{( 2 5 + 2 ) ( 2 5 - 2 )} - \frac{2 5 + 2}{( 2 5 + 2 ) ( 2 5 - 2 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{2 5 - 2 - ( 2 5 + 2 )}{( 2 5 + 2 ) ( 2 5 - 2 )}

Simplify

25 - 2 - (25 + 2) : - 4

= \frac{- 4}{( 2 5 + 2 ) ( 2 5 - 2 )}

Apply Difference of Two Squares

(25 + 2) (25 - 2) : 16

= \frac{- 4}{16}

Cancel

\frac{- 4}{16} : - \frac{1}{4}

= - \frac{1}{4}

cot (θ) sec (θ)

lo g_{4} (lo g_{11} (121) + lo g_{16} (2))

sin^{2} (θ) - cos^{2} (θ)

(tan (x) + cot (x))^{2}

\frac{x}{y} - \frac{3 x}{2 y} + \frac{2 x}{5 y}

What is 1/(2sqrt(5)+2)-1/(2sqrt(5)-2) ?
The solution to 1/(2sqrt(5)+2)-1/(2sqrt(5)-2) is -1/4